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Symbolic-Numeric Implementation of the Method of Collocations and Least Squares for 3D Navier–Stokes Equations

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Computer Algebra in Scientific Computing (CASC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

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Abstract

The method of collocations and least squares, which was previously proposed for the numerical solution of the two-dimensional Navier–Stokes equations governing steady incompressible viscous flows, is extended here for the three-dimensional case. The derivation of the collocation and matching conditions is carried out in symbolic form using the CAS Mathematica. The numerical stages are implemented in a Fortran code, into which the left-hand sides of the collocation and matching equations have been imported from the Mathematica program. The results of numerical tests confirm the second order of convergence of the presented method.

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Author information

Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Vasily P. Shapeev & Evgenii V. Vorozhtsov

Authors
  1. Vasily P. Shapeev
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  2. Evgenii V. Vorozhtsov
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2012 Springer-Verlag Berlin Heidelberg

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Shapeev, V.P., Vorozhtsov, E.V. (2012). Symbolic-Numeric Implementation of the Method of Collocations and Least Squares for 3D Navier–Stokes Equations. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_27

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  • DOI: https://doi.org/10.1007/978-3-642-32973-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32972-2

  • Online ISBN: 978-3-642-32973-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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